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Azagra Rueda, Daniel and Fabián, M. and Jiménez Sevilla, María del Mar
(2005)
*Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces.*
Canadian Mathematical Bulletin, 48
(4).
pp. 481-499.
ISSN 0008-4395

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Official URL: http://cms.math.ca/cmb/

## Abstract

We establish sufficient conditions on the shape of a set A included in

the space Ln s (X; Y ) of the n-linear symmetric mappings between Banach spaces

X and Y , to ensure the existence of a Cn-smooth mapping f : X ¡! Y , with bounded support, and such that f(n)(X) = A, provided that X admits a Cn- smooth bump with bounded n-th derivative and densX = densLn(X; Y ). For instance, when X is infinite-dimensional, every bounded connected and open set U containing the origin is the range of the n-th derivative of such a mapping.

The same holds true for the closure of U, provided that every point in the boundary of U is the end point of a path within U. In the finite-dimensional case, more restrictive conditions are required. We also study the Fr´echet smooth case for mappings from Rn to a separable infinite-dimensional Banach space and the Gˆateaux smooth case for mappings defined on a separable infinite-dimensional

Banach space and with values in a separable Banach space.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Starlike Bodies; Range; Theorem; Bump |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 12927 |

Deposited On: | 11 Jul 2011 08:06 |

Last Modified: | 06 Feb 2014 09:36 |

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